Been a long time since I've been there (1977!), and did not do any mountain trekking but just bummed around with my wife for a couple of months.

From a cultural standpoint I'd highly recommend riding the train from Delhi into Rajahstan, going all the way to Jaisalmer. Lots to see and so on that route - many old Mughal palaces and ruined forts. Also, the Jain temples of Mount Abu are stunning works, that required a bus ride, but Abu was a nice respite from the heat and dust lower down.

The rock temples and caves of Ajanta and Ellora in central India are also astounding. I'm surprised that they are not more well known, but worth a visit.

I'd second visiting Ajunta and Elora, in which case you'd to fly into Bombay.

When I was there you could buy a one-month pass from Air Indian for something like $200, which let you fly all over the place with some limitations (like you couldn't fly back to the same point). Given the really vast distances this is the best way to see as much of the subcontinent as possible. But you'll still have to spend a fair amount of time on buses, trains, etc.

I'd suggest skipping Goa and the west coast.

By far the most interesting city I saw was Varanasi. Many people go overland from there to Nepal, so you might consider making that your last stop. If you have any interest in Buddhism, I'd highly recommend visiting the holy sites in Indian, such as Sarnath outside of Varanasi and especially Bodhgaya to the east.

I'll second Varanasi--a real wild and amazing city, the kind of thing you go to India for. Also, as touristy as it sounds, don't miss the Taj Mahal in Agra. I've been all over, and I think it's the most beautiful building in the world. Most of Rajastan--Jaiper, Udaipur, etc.--is well worth seeing. You can easily do several months just there.

If I go back, one region I'd like to see is Kerala, in the south, very tropical and lush. Darjeeling, on the opposite side of the country looks fantastic as well. Some trekking in the hills above the tea plantations with nice views of Kanchenjunga.

You could also go trekking in the north but the Garwhal is much smaller and the hiking more limited than in Nepal, which will be in fine trekking condition in March. When they're up north, some folks like to go to Lake Tal, rent a houseboat and hang out, but I had a buddy do that who wasn't super happy with the experience. I've also heard people frown at Goa. It's supposedly become kind of a junkie scene, but I'd still like to vist it someday.

I've also seen photos of Elora and that's also high on my list.

India is kind of challenging place to visit. Lots of intense poverty, agressive touts, you might get pretty sick (I did). As rewarding as it was, I was also happy to leave. Afterward, I stopped taking things for granted in my life and learned to appreciate even the simple things far, far more. In short, though, you'll have a blast wherever you go.

One thing I forgot to add: if you're going to Kathmandu directly after India, I'd recommend flying from Varanasi. It'll set you back about $100 but it's two hours vs. a 24 hour bus ride, which I heard others describe as epic.

BTW, I'm not sure what you mean by a limited time in Nepal but, if you're there, you really should invest enough time to go on a substantial trek, either Everest Basecamp or the Annapurna Circuit (which I did). If you're spending four months just in So. America, you're kind of cheating yourself if you don't spend at least a whole month in Nepal. Go trekking, explore Kathmandu and Pokhara, and go to Chitwan and see some rhinos. S. America is nice, but Nepal is,well, Nepal.

If I remember correctly, you can live on ~10 USD/day in India (and Nepal) including everything (food, lodging, travel within the country (train/bus), possible gifts for friends). That is if you do no climbing/trekking. If you hire porters/donkeymen, need to buy supplies/rent equipment, this could go up to ~30 USD/day. Of course this also depends on how high your requirements are

You could easily spend a full month in Rajasthan.

As for 'ruins', in the Delhi/Mumbai area I would recommend Khajuraho, Ellora, Ajanta, Fatehpur Sikri, Orcha among others.

I recommend the LP Trekking in the Indian Himalaya book.

Manali, McLeod Ganj are probably good places to find fellow trekkers at that time of year.

MichaelJ's recommendation on visiting Varanasi and then taking a train+bus+jeep to the Nepali border is a good one. You would then arrive sort of midway between Kathmandu and Pokhara and could also visit Chitwan national park en route.

I enjoyed Goa/Kerala as well, but those are very far south from Bombay/Delhi by train.